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Journal Articles Zeitschrift für Angewandte Mathematik und Physik Year : 2013

Motion of a distant solid particle in a shear flow along a porous slab

Abstract

The motion of a solid and no-slipping particle immersed in a shear flow along a sufficiently porous slab is investigated. The fluid flow outside and inside of the slab is governed by the Stokes and Darcy equations, respectively, and the so-called Beavers and Joseph slip boundary conditions are enforced on the slab surface. The problem is solved for a distant particle with length scale a in terms of the small parameter a/d where d designates the large particle-slab separation. This is achieved by asymptotically inverting a relevant boundary-integral equation on the particle surface, which has been recently proposed for any particle location (distant or close particle) in Khabthani et al. (J Fluid Mech 713:271-306, 2012). It is found that at order O(a/d) the slab behaves for any particle shape as a solid plane no-slip wall while the slab properties (thickness, permeability, associated slip length) solely enter at O((a/d)(2)). Moreover, for a spherical particle, the numerical results published in Khabthani et al. (J Fluid Mech 713:271-306, 2012) perfectly agree with the present asymptotic analysis.

Dates and versions

hal-00996425 , version 1 (30-05-2014)

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Cite

S. Khabthani, Antoine Sellier, F. Feuillebois. Motion of a distant solid particle in a shear flow along a porous slab. Zeitschrift für Angewandte Mathematik und Physik, 2013, 64 (6), pp.1759-1777. ⟨10.1007/s00033-013-0355-8⟩. ⟨hal-00996425⟩
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